## Info

Pressure or speed

### Pressure or speed

Fig. 9.1 Power output and thermal efficiency of Stirling engines as a function of engine speed or pressure level. F fleets of dead volume, harmonic motion, and adiahatic compression and expansion on the ideal cycle the ideal Stirling engine there must he some void volume in the regenerator and other heat exchangers. Including this dead volume reduces the amplitude of the pressure excursion when the working fluid is moved from the cold to the hot space and results in a reduction in the power output per unit mass of working fluid, represented by the line 'B-B' in Fig. 9.1(a). The efficiency remains at the ideal cycle value.

A departure from discontinuous piston motion to the sinusoidal piston motion of the Schmidt isothermal cycle causes a redistribution of the working fluid between the compression, expansion and the dead space with consequent further reduction in the range of the pressure amplitude and power output. This is represented by the line 4C-C in big. 9.1(a). As before, the efficiency remains at the ideal cycle value.

In most of the mechanisms used to effect the volume variations the motion is not exactly sinusoidal. As an example, consider the simple crank slider mechanism shown in Fig. 9.2. The motion of the piston P may be represented by the equation:

(x/r) = (1 -cos 9) + (//r)( 1 -cos <*>) (9.1)

where x is the distance moved by the piston from the outer dead point A. r is the crank radius ! is the length of the connecting rod 0 is the crank angle </> is the connecting rod angle. The second term of the equation is the distortion to true sinusoidal motion of the first term imposed by the crank connecting rod obliquity,

The effect can be minimized by the use of a long connecting rod. but this cannol be taken too far as it leads to long, heavy machines.

The effect of non-sinusoidal piston motion is to further modify the mass distribution of working fluid in the engine and may or may not cause a reduction in the power output depending on the other engine parameters. In many cases the effect of non-sinusoidal piston motion is of secondary importance and often may be neglected, at least at the preliminary design stage.

### Adiabatic cycle

None of the above factors affected the thermal efficiency. We have assumed so far that isothermal conditions exist in both the compression and expansion spaces so the ideal efficiency remains even though the quantities of heat transferred may decrease. However, real engines simply cannot achieve isothermal conditions. The heat transfer is always limited. A better model for high-speed (2000 revolutions per minute) engines may be the Finkelstein adiabatic cycle. This assumes that no heat transfer takes place in the compression and expansion cylinders, i.e. the heat transfer coefficient is zero. In the heater and cooler, however, the rates of heat transfer are assumed to be infinite so the working fluid in those spaces is always at the upper and lower cycle temperatures 7mux and 7mi)I. The cycle is discussed in more detail in Chapter 4.

A conversion from isothermal to adiabatic conditions in the engine cylinder causes a marked redistribution of the cyclic mass variation of the working fluid. The mean temperature in the expansion space is less than in --jothe—cas~ •' erea : mi •mpi je in ' con j;ion space is increased. The work output from the expansion space is therefore decreased, whereas the work input to the compression space is increased. The result is that both the net cycle work and cycle thermal efficiency are reduced as shown by line 'D-D' on Fig. 9.1. The conversion to adiabatic operation has a dramatic effect on the efficiency, sometimes decreasing it to half the isothermal value.

## Solar Stirling Engine Basics Explained

The solar Stirling engine is progressively becoming a viable alternative to solar panels for its higher efficiency. Stirling engines might be the best way to harvest the power provided by the sun. This is an easy-to-understand explanation of how Stirling engines work, the different types, and why they are more efficient than steam engines.

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